GMAT Changed on April 16th - Read about the latest changes here

 It is currently 26 May 2018, 16:13

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002,

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Dec 2010
Posts: 106
Concentration: Marketing, General Management
If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, [#permalink]

### Show Tags

Updated on: 02 Nov 2012, 02:37
3
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:34) correct 33% (01:22) wrong based on 260 sessions

### HideShow timer Statistics

If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?

A. 999
B. 1001
C. 1003
D. 1004
E. 1005

Originally posted by ruturaj on 09 Jul 2011, 02:21.
Last edited by Bunuel on 02 Nov 2012, 02:37, edited 1 time in total.
Renamed the topic, edited the question and moved to PS forum.
TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1472
Location: United States (IN)
Concentration: Strategy, Technology
Re: Faster way to solve such questions [#permalink]

### Show Tags

09 Jul 2011, 03:20
1
KUDOS
993 = 1000 - 7

994 = 1000 - 6

996 = 1000 - 4

997 = 1000 - 3

998 = 1000 - 2

1001 = 1000 + 1

1001 = 1000 + 1

1002 = 1000 + 2

1004 = 1000 + 4

So Sum of terms = (1000 * 9 - 22 + 8) + x

Average = (9000 - 14 + x)/10 = 999

999 = 1000 - 1

So (9000 - 14 + x) = 10000 - 10

=> x = 1000 + 4 = 1004

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Joined: 31 Dec 1969
Location: Russian Federation
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)
Re: Faster way to solve such questions [#permalink]

### Show Tags

09 Jul 2011, 03:36
As avg is given we can divide them in 2 groups
1st is of elements below 999 and 2nd is ofelements abv 999
if we find now the diff that each element has with 999
that is (999-each element) for the 1st group (eg. 999-998=1,999-997=2,....)
and (each element-999) for the 2nd group(eg. 1001-999=2,1002-999,....)
now add the diff for each group separately

for 1st group sum is 17 and for 2nd group its 12

17-12=5

so we need an element which is in the 2nd group and 5 more than 999 thats 1004

This method relies on the fact that avg is the middle point of a set from Weightage point of view....
I think this way it cab be solved within a min...
Current Student
Joined: 26 May 2005
Posts: 533
Re: Faster way to solve such questions [#permalink]

### Show Tags

09 Jul 2011, 03:42
4
KUDOS
4
This post was
BOOKMARKED
ruturaj wrote:
If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?
999
1001
1003
1004
1005

I think the fastest way to do this is a simple understanding of mean .
Sum of the deviations of the numbers in the set from the mean is always zero

993, 994, 996, 997, 998, 1001, 1001, 1002, 1004

mean is 999

so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 999+ 5 1004

D
Current Student
Joined: 08 Jan 2009
Posts: 309
GMAT 1: 770 Q50 V46
Re: Faster way to solve such questions [#permalink]

### Show Tags

09 Jul 2011, 05:22
2
KUDOS
$$\frac{3 + 4 + 6 + 7 + 8 + 11 + 11 + 12 + 14 + x}{10} = 9$$

$$\frac{76 + x}{10} = 9$$

$$x = 90 - 76 = 14$$

$$990 + 14 = 1004$$
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8079
Location: Pune, India
Re: Faster way to solve such questions [#permalink]

### Show Tags

13 Jul 2011, 05:00
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
ruturaj wrote:
If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?
999
1001
1003
1004
1005

When I say the mean of the ages of a group is 25, it means that effectively every person's age can be replaced by 25 and the sum of ages will remain the same. The sum of deviation of all numbers from the mean is 0. Deviation means how much the number is more or less than the mean.

If mean is 999, deviation of 993 from mean is -6.
Deviation of 994 from mean is -5.
The sum of all deviations except that of x is:
- 6 - 5 - 3 - 2 - 1 + 2+ 2 + 3 + 5 = -5
But this sum should be 0. Hence deviation of x from 999 should be +5. Therefore, x should be 1004.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 29 Sep 2012
Posts: 20
Location: United States
Concentration: Finance, Strategy
WE: Corporate Finance (Investment Banking)
Re: Faster way to solve such questions [#permalink]

### Show Tags

01 Nov 2012, 22:59
ruturaj wrote:
If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?
999
1001
1003
1004
1005

This problem can be solved in 8 secs

When you have sequences like this with very little differences we may deviate with signs and differences.
To get rid of them and wasting time in adding big numbers, we can replace these big numbers with very small numbers.

Remember, every sec in GMAT is Invaluable

example:
If 993(the first term) is assumed as 1, 994 --> 993+1 is replaced by 1+1 ie 2, and so on so forth,then the sequence will be

Mean is 999 which is 993+6 ie 1+6=7

(1+2+4+5+6+9+9+10+12+x)/10=7
x=12, which is 1 + 11 = 993+11= 1004

_________________

Learn the Values. Knowledge comes by itself.

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, [#permalink]

### Show Tags

01 Oct 2014, 03:33
Mean = 999

Dividing the numbers in 2 groups; < 999 & > 999

Group I : < 999

999-6 = 993

999-5 = 994

999-3 = 996

999-2 = 997

999-1 = 998

Total -ve = -17

Group II: > 999

999+2 = 1001

999+2 = 1001

999+3 = 1002

999+5 = 1004

Total +ve = 12

For the mean (including x) to be 999, total +ve should be equal to total -ve

So, 999+5 = 1004

_________________

Kindly press "+1 Kudos" to appreciate

Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, [#permalink]

### Show Tags

14 Feb 2015, 05:59
Great tips! I did it somehow different:

993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 , x | M = 999

1000*4...=.4000
900*5.....=.4500
90*5.......=..450
+28........=....28
+8..........=.....8

$$\frac{8986+x}{10}$$= 999

x = 1004
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2442
Re: If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, [#permalink]

### Show Tags

12 Feb 2018, 17:36
ruturaj wrote:
If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?

A. 999
B. 1001
C. 1003
D. 1004
E. 1005

Since the numbers are “pretty” large and each is “pretty” close to the average, without using the conventional formula (i.e., average = sum/quantity), we can determine the value of x by using the difference between each known number and the average. If we subtract 999, the average, from each number, we have:

-6, -5, -3, -2, -1, 2, 2, 3, 5

We see that the sum of the differences is (-17) + 12 = -5. To counter the -5 (i.e., 5 less than the average), we need a value that is 5 more than the average. That is, we need x to be 999 + 5 = 1004 so that the average of all values (including x) will be 999.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002,   [#permalink] 12 Feb 2018, 17:36
Display posts from previous: Sort by